if two particles have equal kenetic energies, do they have the same momentum?
NO! Just because something has the same kinetic energy doesn't mean it has the same momentum. There are a number of factors that could affect it.
Kinetic energy of an object with mass m and velocity v is (1/2)mv2. Momentum is mv.
Take for example, an object with mass 4kg and speed 1 m/s. Its kinetic energy is (1/2)(4)(1)2= 2 Joules and its momentum is (4)(1)= 4 kgm/s. Take a second object with mass 1kg and speed 2 m/s. It has kinetic energy (1/2)(1)(2)2= 2 Joules also but its momentum is (1)(2)= 2 kgm/s.
Well, kinetic energy (for particles, as the question originally asked) is probably more likely to be [itex] K = (\gamma - 1) mc^2[/itex], i.e. relativistic kinetic energy, which reduces to the Newtonian expression in the limit of small v.
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